Throughout this description various publications are cited as representative of related art. For the sake of simplicity, these documents will be referred by reference numbers enclosed in square brackets, e.g., [x]. A complete list of these publications ordered according to the reference numbers is reproduced in the section entitled “List of references” at the end of the description. These publications are incorporated by reference herein.
In digital transmission systems, one technique to transmit source bits is to group them into complex symbols representing the amplitude and phase of the signal modulating a frequency carrier. QAM (quadrature amplitude modulation) and PSK (phase shift keying) are examples. QAM (PSK) complex symbols are associated with m binary bits; overall, the way the bits are associated with the M2=2m complex symbols is called “mapping”, while the set of symbols is called a “constellation”. For example, QPSK (quadrature phase shift keying) refers to 4 complex symbols representable through the two-bit values 00, 01, 10, 11 respectively. Similarly M2-QAM constellation, e.g., 16-QAM, refers to the symbols originated by all possible groups of 4 bits 0000, 0001, 1100, etc. Gray mapping is a well-known example technique wherein two adjacent complex symbols represent group of bits differing by at most 1 bit. Complex symbols may be graphically represented in the complex plane where the two axes represent the in-phase (I) and quadrature-phase (Q) components of the complex symbol. FIG. 1 shows an example QPSK constellation, representing bits through Gray mapping rule, and a possible received symbol.
Digital data (bits or symbols) are transmitted through physical channels that normally corrupt them because of additive noise. Moreover in wireless systems, the experienced fading channel imposes distortion (i.e., phase and amplitude changes). For these reasons the received data may not coincide with the transmitted ones and an equalization technique may be used to estimate the transmitted data. Normally the channel coefficients are estimated prior to such equalization and assumed known by the equalizer. The robustness of a transmission link depends on the ability of the receiver to reliably detect the transmitted bits (i.e., transmitted 1s as 1s and 0s as 0s).
At the transmitter side, encoding through error correction codes (ECGs) is a common technique to increase the robustness of the link to noise corruption. At the receiver side it, implies the use of ECC decoders to correctly identify the transmitted bits.
ECC decoders typically provide better performance, i.e., are able to detect the originally transmitted bits with more reliability, if they process input bit “soft” decisions (i.e., probabilities of having received 1 or 0) rather than “hard” input (i.e., received bits already interpreted to be 1 or 0). Examples include the well-known soft-input Viterbi algorithm, Low Density Parity Check Codes (LDPCC), and Turbo Codes (TC). In wireless systems, soft decisions are computed based on the received symbol, the channel coefficient estimates, and the noise-variance estimate.
Wireless transmission through multiple antennas, also referred to as MIMO (Multiple-Input Multiple-Output), currently enjoys great popularity because of the demand of high data-rate communication from multimedia services. MIMO transmission includes of the simultaneous transmission of T complex symbols using T transmit antennas; this way a transmit data rate of T times the data rate of a single antenna system transmitting in the same bandwidth may be obtained. In the following, the sequence of T symbols simultaneously transmitted by the multiple antennas will be also referred to as “transmit sequence” or “transmit vector”. In one example, each individual symbol is a sample of the mentioned PSK or QAM constellations. Normally R≧T receive antennas are employed to receive the transmit sequence. The R received symbols will be also referred to as “received sequence” or “vector” (of symbols or signals). FIGS. 2A and 2B illustrate example systems for MIMO transmission and reception.
Then, receivers for MIMO wireless receive as input at each receive antenna a signal made of the superposition of simultaneously transmitted symbols, each signal distorted by the channel and corrupted by noise. A schematic example of a MIMO system representation for two transmit and two receive antennas is shown in FIG. 3, where the multiple channel links, the transmit vector, and the received vector are evidenced.
Therefore a fundamental part of MIMO receivers is dedicated to perform “spatial equalization” meaning that starting from the input received vector and the channel coefficients estimates, the transmit sequence is estimated, or “detected”. A method or apparatus implementing a technique to detect a transmit sequence is called a (MIMO) “detector” in the literature. If the output is an estimate {circumflex over (x)} of the transmit sequence X of symbols, it is called a “hard output” (or a “hard decision”) detector. If, in addition (or in alternative), it also generates bit soft-output information (or log-likelihood ratios, LLRs, in the logarithmic domain), as typically required in digital communications featuring soft-input ECC decoders, then the detector is said to be a “soft-output” detector. The two options are portrayed in FIGS. 4A and 4B respectively.